As a settlement for an insurance? claim, Craig was offered one of two choices. He could either accept a? lump-sum amount of ?$4809 ?now, or accept quarterly payments of ?$165 for the next eight years. If the money is placed into a trust fund earning 3.63?% compounded semi-annually?, which is the better option and by how? much?

 

Lumpsum amount is the better option and is higher by $241.45

Step-by-step explanation

1.Convert the given rate into effective rate with semi-annual compounding

Effective rate=(1+APR/m)^m-1

= (1+3.63%/2)^2-1

= 0.0366294225

2.Convert effective rate into Nominal rate with quarterly compounding

Effective rate=(1+APR/m)^m-1

0.0366294225= (1+APR/4)^4-1

APR=4*( (1+0.0366294225)^(1/4)-1)

=0.03613676676

3. Find the present value of quarterly payments

PV= Payment*(1-1/(1+r)^n)/r

= 165*(1-1/(1+0.03613676676/4)^(8*4))/(0.03613676676/4)

=165*27.68211142

= $4,567.55

4. Lumpsum amount is higher by $241.45

(4809-4567.55)

Excel method for better understanding

Please see the attached file for the complete solution